Modern pension design by refundable income tontines

Life and pension annuities often contain a "safety net" in case of an early death in the retirement phase. Within a specified guarantee period, parts of the paid premium are refunded as a bequest. Such a guarantee may increase the attractiveness of retirement products, helping to reduce concerns from (risk-averse) policyholders as well as regulators. We show how to include such a guarantee into a tontine fund (also named pooled annuity, collective defined contribution or group-self annuitization scheme), without leaving any risks with the insurance provider. This product is compared to refundable income annuities, where payments and bequests are fully guaranteed to policyholders. Given the reluctance of states, employers and pension funds to provide long-term guarantees, a pooled annuity fund with premium-refund guarantee may be a way to complement existing state pensions by an additional funded layer. The results have implications for the design of collective defined contribution plans where policyholders with different risk characteristics (age, health) share risks fairly.